@inbook{3b724b57a54b49a2ba6629cbcf7a1bde,
title = "Operator-valued slice hyperholomorphic functions",
abstract = "In this chapter we introduce slice hyperholomorphic functions with values in a quaternionic Banach space. As in the complex case, there are two equivalent notions, namely weak and strong slice hyperholomorphicity. In order to properly define a multiplication between slice hyperholomorphic functions, we give a third characterization in terms of the Cauchy–Riemann system. Operator-valued functions can be obtained by using the so-called S-functional calculus. This calculus is associated with the notions of S-spectrum and S-resolvent, which are introduced and studied. We also present some hyperholomorphic extension results and, finally, we study the Hilbert-space-valued quaternionic Hardy space of the ball and its backward-shift invariant subspaces.",
author = "Daniel Alpay and Fabrizio Colombo and Irene Sabadini",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-42514-6_7",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer International Publishing",
pages = "165--194",
booktitle = "Operator Theory",
}